多组分玻色-爱因斯坦凝聚体中$SO(2)$诱导的呼吸模式
$SO(2)$-induced breathing patterns in multi-component Bose-Einstein condensates
摘要：
在这项工作中，我们使用的$SO(2)$ -旋转的两个组件，一个，两个和三维的非线性薛定谔系统在Manakov极限和附近，构造矢量孤子和涡旋结构。这样，稳定的稳态暗-亮孤子和它们的高维同胞被转化为鲁棒的振荡暗-暗孤子（及其推广），有和没有谐波限制。通过与一维情况类比，矢量高维结构在二维中采取涡-涡状态的形式，例如，涡环-三维涡环。我们考虑了不相等（自相互作用和交叉相互作用）强度的影响，其中仅近似满足$SO(2)$对称性，表明暗-暗孤立子振荡通常是稳健的。类似的特征在更高的维度中也被发现，尽管我们的例子表明相分离等现象可能有助于相关的动力学。这些结果，与光学和玻色-爱因斯坦凝聚体（BECs）中这种状态的一维变体的实验实现有关，表明本文提出的高维束缚态的潜在观察。
英文摘要：
In this work, we employ the $SO(2)$-rotations of a two-component, one-, two- and three-dimensional nonlinear Schrödinger system at and near the Manakov limit, to construct vector solitons and vortex structures. This way, stable stationary dark-bright solitons and their higher-dimensional siblings are transformed into robust oscillatory dark-dark solitons (and generalizations thereof), with and without a harmonic confinement. By analogy to the one-dimensional case, vector higher-dimensional structures take the form of vortex-vortex states in two dimensions and, e.g., vortex ring-vortex ring ones in three dimensions. We consider the effects of unequal (self- and cross-) interaction strengths, where the $SO(2)$ symmetry is only approximately satisfied, showing the dark-dark soliton oscillation is generally robust. Similar features are found in higher dimensions too, although our case examples suggest that phenomena such as phase separation may contribute to the associated dynamics. These results, in connection with the experimental realization of one-dimensional variants of such states in optics and Bose-Einstein condensates (BECs), suggest the potential observation of the higher-dimensional bound states proposed herein.
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